PHYSICS: Minimum Velocity

Question

What is the minimum velocity required of a roller coaster at the top of a vertical loop with a radius of 7 m?

 

SHOW ALL WORK PLEASE.

May use if needed:

Fc = Fn + Fg

Fc = MAc

Ac = v^2/r

Answer 1

For velocity to be minimum at the top, the normal force must be zero.

 

Fc = N+W = W = mg

 

m v^2 / r = mg

 

Hence,

 

v^2 / r = g

 

v = sqrt(rg) = sqrt(7m * 9.8 m/s^2) = 8.28 m/s